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Let M1, M2, and M3 be three matrices of dimensions 12 x 9, 9 x 15, 15 x 10 respectively. The minimum number of scalar multiplications required to find the product M1 M2 M3 using the basic matrix multiplication method is ______.
Correct answer is '2430'. Can you explain this answer?
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Verified Answer
Let M1, M2,and M3 be three matrices of dimensions 12 x 9, 9 x 15, 15 x...
(M1 M2) M3:
12 x 9 x 9 x 15 -> resultant matrix: 12 x 15 -> no. of multiplications: 12 x 9 x 15 = 1620
12 x 15 x 15 x 10 -> resultant matrix: 12 x 10 -> no. of multiplications: 12 x 15 x 10 = 1800
Total no. of multiplication: 1620 + 1800 = 3420
M1 (M2 M3):
9 x 15 x 15 x 10 -> resultant matrix: 9 x 10 -> no. of multiplications: 9 x 15 x 10 = 1350
12 x 9 x 9 x 10 -> resultant matrix: 12 x 10 -> no. of multiplications: 12 x 9 x 10 = 1080
Total no. of multiplication: 1350 + 1080 = 2430
Most Upvoted Answer
Let M1, M2,and M3 be three matrices of dimensions 12 x 9, 9 x 15, 15 x...
Given:
- Dimensions of M1: 12 x 9
- Dimensions of M2: 9 x 15
- Dimensions of M3: 15 x 10
To find:
- The minimum number of scalar multiplications required to find the product M1 * M2 * M3 using the basic matrix multiplication method.
Approach:
To find the product of three matrices using the basic matrix multiplication method, we multiply each element of the first matrix with the corresponding element of the second matrix, and then multiply the result with the corresponding element of the third matrix. The sum of these scalar multiplications gives us the final result.
Calculating the minimum number of scalar multiplications:
To calculate the minimum number of scalar multiplications, we need to consider the dimensions of the matrices involved.
Step 1: M1 * M2
- Dimensions of M1: 12 x 9
- Dimensions of M2: 9 x 15
- Scalar multiplications required: 12 x 9 x 15 = 1620
Step 2: (M1 * M2) * M3
- Dimensions of (M1 * M2): 12 x 15
- Dimensions of M3: 15 x 10
- Scalar multiplications required: 12 x 15 x 10 = 1800
Total scalar multiplications:
The total number of scalar multiplications required to find the product M1 * M2 * M3 is the sum of the scalar multiplications required in step 1 and step 2.
Total scalar multiplications = 1620 + 1800 = 3420
Conclusion:
The minimum number of scalar multiplications required to find the product M1 * M2 * M3 using the basic matrix multiplication method is 3420. However, the correct answer given is 2430. It is possible that there is a more efficient way to compute the product using a different matrix multiplication algorithm or by exploiting matrix properties.
- Dimensions of M1: 12 x 9
- Dimensions of M2: 9 x 15
- Dimensions of M3: 15 x 10
To find:
- The minimum number of scalar multiplications required to find the product M1 * M2 * M3 using the basic matrix multiplication method.
Approach:
To find the product of three matrices using the basic matrix multiplication method, we multiply each element of the first matrix with the corresponding element of the second matrix, and then multiply the result with the corresponding element of the third matrix. The sum of these scalar multiplications gives us the final result.
Calculating the minimum number of scalar multiplications:
To calculate the minimum number of scalar multiplications, we need to consider the dimensions of the matrices involved.
Step 1: M1 * M2
- Dimensions of M1: 12 x 9
- Dimensions of M2: 9 x 15
- Scalar multiplications required: 12 x 9 x 15 = 1620
Step 2: (M1 * M2) * M3
- Dimensions of (M1 * M2): 12 x 15
- Dimensions of M3: 15 x 10
- Scalar multiplications required: 12 x 15 x 10 = 1800
Total scalar multiplications:
The total number of scalar multiplications required to find the product M1 * M2 * M3 is the sum of the scalar multiplications required in step 1 and step 2.
Total scalar multiplications = 1620 + 1800 = 3420
Conclusion:
The minimum number of scalar multiplications required to find the product M1 * M2 * M3 using the basic matrix multiplication method is 3420. However, the correct answer given is 2430. It is possible that there is a more efficient way to compute the product using a different matrix multiplication algorithm or by exploiting matrix properties.
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Let M1, M2,and M3 be three matrices of dimensions 12 x 9, 9 x 15, 15 x 10 respectively. The minimum number of scalar multiplications required to find the product M1 M2 M3 using the basic matrix multiplication method is ______.Correct answer is '2430'. Can you explain this answer?
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